Question: Solve for $x$ and $y$ using elimination. ${6x-3y = 6}$ ${5x+3y = 60}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $11x = 66$ $\dfrac{11x}{{11}} = \dfrac{66}{{11}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {6x-3y = 6}\thinspace$ to find $y$ ${6}{(6)}{ - 3y = 6}$ $36-3y = 6$ $36{-36} - 3y = 6{-36}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 6}$ into $\thinspace {5x+3y = 60}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + 3y = 60}$ ${y = 10}$